Answer:
(A) - (5)
(B) - (4)
(C) - (1)
(D) - (2)
Step-by-step explanation:
(A) We are given the polynomial (x+4)(x−4)[x−(2−i)][x−(2+i)]
(5) The related polynomial equation has a total of four roots; two roots are complex and two roots are real.
(B) We are given the polynomial (x+i)(x−i)(x−2)³(x−4).
(4) The related polynomial equation has a total of six roots; two roots are complex and one of the remaining real roots has a multiplicity of 3.
(C) We are given the polynomial (x+3)(x−5)(x+2)²
(1) The related polynomial equation has a total of four roots; all four roots are real and one root has a multiplicity of 2.
(D) We are given the polynomial (x+2)²(x+1)²
(2) The related polynomial equation has a total four roots; all four roots are real and two roots have a multiplicity of 2. (Answer)
Answer:
78 x 160
/100
= 124.8
12 x 325/100
= 39
Step-by-step explanation:
The price of the sweater was reduced by 40%
Step-by-step explanation:
Step 1; Cost before reduction was $20. The cost after reduction was 12$. Cost reduced= cost before reduction - cost after reduction
Cost reduced= $20 - $12 = $8
Step 2; We must find how much of the cost was reduced from the initial cost i.e. how much $8 is to $20. To do this we must convert it into a percentage. We divide the $8 with the $20 to get a value. This value must be multiplied with a 100 to be converted into a percentage.
Cost by which sweater was reduced= 
* 100 = 0.4 * 100 = 40
So the price of the sweater was reduced from $20 to $8 which equates to a reduction in 40%.
This question requires creating a few equations and working through them step-by-step. Now, first let's give each of the shapes a variable: let's say that the blue shape is a, the orange shape is b and the green shape is c.
1. We can technically create six formulas for the magic square, with three for sum of the rows and three for the sum of the columns, however the smartest way to approach this is to observe whether there are any obvious answers that we can get.
We can see in row 2 that there are three of the same shape (a) that add to 57. This makes it very simple to calculate the value of the shape.
Since 3a = 57
a = 57/3 = 19
2. Now we need to find a row or column that includes a and one other shape; we could choose either column 2 or 3, so let's go with column 2. Remembering that the blue shape is a and the orange shape is b:
2a + b = 50
Now, given that a = 19:
2(19) + b = 50
38 + b = 50
b = 12
3. We can now take any of the rows or columns that include the third shape (c) since we already know the values of the other two shapes. Let's take column 1:
a + b + c = 38
19 + 12 + c = 38
31 + c = 38
c = 38 - 31
c = 7
Thus, the value of the blue shape is 19, the value of the orange shape is 12 and the value of the green shape is 7.
Answer: slope of segment KL = slope of segment MN
Step-by-step explanation:
we know that a parallelogram always have two pairs of opposite sides that are parallel and therefore the slopes of the opposite sides must be same to be parallel to each other.
